%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET759+4 : TPTP v8.1.2. Bugfixed v2.2.1. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n015.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 15:26:19 EDT 2023 % Result : Theorem 11.79s 2.26s % Output : Proof 14.78s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET759+4 : TPTP v8.1.2. Bugfixed v2.2.1. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n015.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Sat Aug 26 10:09:52 EDT 2023 % 0.12/0.34 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.35/1.16 Prover 4: Preprocessing ... % 3.78/1.18 Prover 1: Preprocessing ... % 3.78/1.20 Prover 5: Preprocessing ... % 3.78/1.20 Prover 0: Preprocessing ... % 3.78/1.20 Prover 2: Preprocessing ... % 3.78/1.20 Prover 6: Preprocessing ... % 3.78/1.20 Prover 3: Preprocessing ... % 8.67/1.85 Prover 2: Proving ... % 8.67/1.86 Prover 5: Proving ... % 9.09/1.91 Prover 6: Proving ... % 9.62/1.99 Prover 3: Constructing countermodel ... % 9.62/1.99 Prover 1: Constructing countermodel ... % 11.79/2.26 Prover 3: proved (1626ms) % 11.79/2.26 % 11.79/2.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.79/2.26 % 11.79/2.27 Prover 2: stopped % 11.79/2.28 Prover 5: stopped % 11.79/2.28 Prover 6: stopped % 12.05/2.30 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 12.05/2.30 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 12.05/2.30 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.05/2.30 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.05/2.33 Prover 7: Preprocessing ... % 12.35/2.34 Prover 8: Preprocessing ... % 12.35/2.36 Prover 10: Preprocessing ... % 12.35/2.37 Prover 11: Preprocessing ... % 12.87/2.44 Prover 7: Warning: ignoring some quantifiers % 13.34/2.48 Prover 10: Warning: ignoring some quantifiers % 13.34/2.50 Prover 1: Found proof (size 96) % 13.34/2.50 Prover 1: proved (1870ms) % 13.34/2.51 Prover 7: Constructing countermodel ... % 13.34/2.51 Prover 10: Constructing countermodel ... % 13.34/2.52 Prover 11: stopped % 13.34/2.52 Prover 10: stopped % 13.34/2.53 Prover 4: Constructing countermodel ... % 13.34/2.54 Prover 7: stopped % 13.34/2.55 Prover 0: Proving ... % 13.34/2.55 Prover 0: stopped % 13.34/2.56 Prover 4: stopped % 14.23/2.60 Prover 8: Warning: ignoring some quantifiers % 14.23/2.61 Prover 8: Constructing countermodel ... % 14.23/2.62 Prover 8: stopped % 14.23/2.62 % 14.23/2.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.23/2.62 % 14.23/2.63 % SZS output start Proof for theBenchmark % 14.23/2.63 Assumptions after simplification: % 14.23/2.63 --------------------------------- % 14.23/2.63 % 14.23/2.63 (equal_set) % 14.42/2.66 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) = % 14.42/2.66 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1, % 14.42/2.66 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0: % 14.42/2.66 $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 14.42/2.66 (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 14.42/2.66 % 14.42/2.66 (image3) % 14.42/2.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 14.42/2.66 int] : (v5 = 0 | ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = v5) | % 14.42/2.66 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ( ~ (v6 = 0) & % 14.42/2.66 member(v3, v2) = v6) | ! [v6: $i] : ( ~ (apply(v0, v6, v3) = 0) | ~ % 14.42/2.66 $i(v6) | ? [v7: int] : ( ~ (v7 = 0) & member(v6, v1) = v7))) & ! [v0: % 14.42/2.66 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 14.42/2.66 (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ~ $i(v3) | ~ $i(v2) % 14.42/2.66 | ~ $i(v1) | ~ $i(v0) | (member(v3, v2) = 0 & ? [v5: $i] : (apply(v0, v5, % 14.42/2.66 v3) = 0 & member(v5, v1) = 0 & $i(v5)))) % 14.42/2.66 % 14.42/2.66 (injective) % 14.42/2.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 14.42/2.67 (injective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 14.42/2.67 $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v5 = v4) & apply(v0, v5, v6) = 0 & % 14.42/2.67 apply(v0, v4, v6) = 0 & member(v6, v2) = 0 & member(v5, v1) = 0 & % 14.42/2.67 member(v4, v1) = 0 & $i(v6) & $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: % 14.42/2.67 $i] : ! [v2: $i] : ( ~ (injective(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) % 14.42/2.67 | ~ $i(v0) | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v3 | ~ % 14.42/2.67 (apply(v0, v4, v5) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ $i(v5) | ~ % 14.42/2.67 $i(v4) | ~ $i(v3) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 14.42/2.67 (member(v5, v2) = v8 & member(v4, v1) = v7 & member(v3, v1) = v6 & ( ~ (v8 % 14.42/2.67 = 0) | ~ (v7 = 0) | ~ (v6 = 0))))) % 14.42/2.67 % 14.42/2.67 (inverse_image3) % 14.42/2.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 14.42/2.67 int] : (v5 = 0 | ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = % 14.42/2.67 v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ( ~ % 14.42/2.67 (v6 = 0) & member(v3, v2) = v6) | ! [v6: $i] : ( ~ (apply(v0, v3, v6) = % 14.42/2.67 0) | ~ $i(v6) | ? [v7: int] : ( ~ (v7 = 0) & member(v6, v1) = v7))) & % 14.42/2.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 14.42/2.67 (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ~ $i(v3) | ~ % 14.42/2.67 $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v3, v2) = 0 & ? [v5: $i] : % 14.42/2.67 (apply(v0, v3, v5) = 0 & member(v5, v1) = 0 & $i(v5)))) % 14.42/2.67 % 14.42/2.67 (maps) % 14.42/2.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 14.42/2.67 (maps(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 14.42/2.67 ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) & apply(v0, v4, v6) = 0 & apply(v0, % 14.42/2.67 v4, v5) = 0 & member(v6, v2) = 0 & member(v5, v2) = 0 & member(v4, v1) = % 14.42/2.67 0 & $i(v6) & $i(v5) & $i(v4)) | ? [v4: $i] : (member(v4, v1) = 0 & $i(v4) % 14.42/2.67 & ! [v5: $i] : ( ~ (apply(v0, v4, v5) = 0) | ~ $i(v5) | ? [v6: int] : ( % 14.42/2.67 ~ (v6 = 0) & member(v5, v2) = v6)))) & ! [v0: $i] : ! [v1: $i] : ! % 14.42/2.67 [v2: $i] : ( ~ (maps(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( % 14.42/2.67 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (apply(v0, v3, v5) % 14.42/2.67 = 0) | ~ (apply(v0, v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) % 14.42/2.67 | ? [v6: any] : ? [v7: any] : ? [v8: any] : (member(v5, v2) = v8 & % 14.42/2.67 member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) % 14.42/2.67 | ~ (v6 = 0)))) & ! [v3: $i] : ( ~ (member(v3, v1) = 0) | ~ % 14.42/2.67 $i(v3) | ? [v4: $i] : (apply(v0, v3, v4) = 0 & member(v4, v2) = 0 & % 14.42/2.67 $i(v4))))) % 14.42/2.67 % 14.42/2.67 (subset) % 14.42/2.68 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 14.42/2.68 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 14.42/2.68 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 14.42/2.68 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 14.42/2.68 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 14.42/2.68 % 14.42/2.68 (thIIa09) % 14.42/2.68 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 14.42/2.68 $i] : ? [v6: int] : ( ~ (v6 = 0) & inverse_image3(v0, v4, v1) = v5 & % 14.42/2.68 image3(v0, v3, v2) = v4 & injective(v0, v1, v2) = 0 & maps(v0, v1, v2) = 0 & % 14.42/2.68 equal_set(v5, v3) = v6 & subset(v3, v1) = 0 & $i(v5) & $i(v4) & $i(v3) & % 14.42/2.68 $i(v2) & $i(v1) & $i(v0)) % 14.42/2.68 % 14.42/2.68 (function-axioms) % 14.42/2.69 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 14.42/2.69 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | % 14.42/2.69 ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) | ~ % 14.42/2.69 (compose_predicate(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: % 14.42/2.69 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 14.42/2.69 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (isomorphism(v6, v5, % 14.42/2.69 v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 14.42/2.69 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 14.42/2.69 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (decreasing(v6, v5, % 14.42/2.69 v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 14.42/2.69 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 14.42/2.69 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (increasing(v6, v5, % 14.42/2.69 v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 14.42/2.69 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 14.42/2.69 ! [v6: $i] : (v1 = v0 | ~ (compose_function(v6, v5, v4, v3, v2) = v1) | ~ % 14.42/2.69 (compose_function(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : % 14.42/2.69 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 14.42/2.69 $i] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ % 14.42/2.69 (inverse_predicate(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 14.42/2.69 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 14.42/2.69 $i] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, % 14.42/2.69 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 14.42/2.69 $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ % 14.42/2.69 (inverse_image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 14.42/2.69 : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ % 14.42/2.69 (image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 14.42/2.69 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | % 14.42/2.69 ~ (inverse_function(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 14.42/2.69 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 14.42/2.69 ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0)) & ! % 14.42/2.69 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 14.42/2.69 $i] : ! [v4: $i] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ % 14.42/2.69 (surjective(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.42/2.69 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 14.42/2.69 (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0)) & ! [v0: % 14.42/2.69 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 14.42/2.69 : ! [v4: $i] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = % 14.42/2.69 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 14.42/2.69 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | % 14.42/2.69 ~ (apply(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 14.42/2.69 [v3: $i] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ % 14.42/2.69 (inverse_image2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 14.42/2.69 ! [v3: $i] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0)) & % 14.42/2.69 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 14.42/2.69 [v3: $i] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0)) % 14.42/2.69 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.42/2.69 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 14.42/2.69 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.42/2.69 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 14.42/2.69 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 14.42/2.69 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 14.42/2.69 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 14.42/2.69 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 14.42/2.69 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 14.42/2.69 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.42/2.69 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 14.42/2.69 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 14.42/2.69 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.42/2.69 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 14.42/2.69 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 14.42/2.69 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 14.42/2.69 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 14.42/2.69 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 14.42/2.69 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 14.42/2.69 (power_set(v2) = v0)) % 14.42/2.69 % 14.42/2.69 Further assumptions not needed in the proof: % 14.42/2.69 -------------------------------------------- % 14.42/2.69 compose_function, compose_predicate, decreasing_function, difference, empty_set, % 14.42/2.69 equal_maps, identity, image2, increasing_function, intersection, % 14.42/2.69 inverse_function, inverse_image2, inverse_predicate, isomorphism, one_to_one, % 14.42/2.69 power_set, product, singleton, sum, surjective, union, unordered_pair % 14.42/2.69 % 14.42/2.69 Those formulas are unsatisfiable: % 14.42/2.69 --------------------------------- % 14.42/2.69 % 14.42/2.69 Begin of proof % 14.42/2.69 | % 14.42/2.69 | ALPHA: (subset) implies: % 14.42/2.69 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ % 14.42/2.69 | $i(v0) | ! [v2: $i] : ( ~ (member(v2, v0) = 0) | ~ $i(v2) | % 14.42/2.69 | member(v2, v1) = 0)) % 14.42/2.69 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 14.42/2.69 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 14.42/2.69 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 14.42/2.69 | % 14.42/2.69 | ALPHA: (equal_set) implies: % 14.42/2.69 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, % 14.42/2.69 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 14.42/2.69 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 14.42/2.69 | 0)))) % 14.42/2.69 | % 14.42/2.69 | ALPHA: (maps) implies: % 14.42/2.70 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (maps(v0, v1, v2) = 0) | % 14.42/2.70 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! [v4: $i] : ! % 14.42/2.70 | [v5: $i] : (v5 = v4 | ~ (apply(v0, v3, v5) = 0) | ~ (apply(v0, % 14.42/2.70 | v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: % 14.42/2.70 | any] : ? [v7: any] : ? [v8: any] : (member(v5, v2) = v8 & % 14.42/2.70 | member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ % 14.42/2.70 | (v7 = 0) | ~ (v6 = 0)))) & ! [v3: $i] : ( ~ (member(v3, v1) % 14.42/2.70 | = 0) | ~ $i(v3) | ? [v4: $i] : (apply(v0, v3, v4) = 0 & % 14.42/2.70 | member(v4, v2) = 0 & $i(v4))))) % 14.42/2.70 | % 14.42/2.70 | ALPHA: (injective) implies: % 14.42/2.70 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (injective(v0, v1, v2) = % 14.42/2.70 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ! [v4: $i] % 14.42/2.70 | : ! [v5: $i] : (v4 = v3 | ~ (apply(v0, v4, v5) = 0) | ~ (apply(v0, % 14.42/2.70 | v3, v5) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: any] % 14.42/2.70 | : ? [v7: any] : ? [v8: any] : (member(v5, v2) = v8 & member(v4, % 14.42/2.70 | v1) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | % 14.42/2.70 | ~ (v6 = 0))))) % 14.42/2.70 | % 14.42/2.70 | ALPHA: (image3) implies: % 14.42/2.70 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 14.42/2.70 | ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ~ $i(v3) | % 14.42/2.70 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v3, v2) = 0 & ? [v5: $i] % 14.42/2.70 | : (apply(v0, v5, v3) = 0 & member(v5, v1) = 0 & $i(v5)))) % 14.42/2.70 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 14.42/2.70 | ! [v5: int] : (v5 = 0 | ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, % 14.42/2.70 | v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 14.42/2.70 | [v6: int] : ( ~ (v6 = 0) & member(v3, v2) = v6) | ! [v6: $i] : ( ~ % 14.42/2.70 | (apply(v0, v6, v3) = 0) | ~ $i(v6) | ? [v7: int] : ( ~ (v7 = 0) & % 14.42/2.70 | member(v6, v1) = v7))) % 14.42/2.70 | % 14.42/2.70 | ALPHA: (inverse_image3) implies: % 14.42/2.70 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 14.42/2.70 | ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ~ % 14.42/2.70 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v3, v2) = 0 & ? % 14.42/2.70 | [v5: $i] : (apply(v0, v3, v5) = 0 & member(v5, v1) = 0 & $i(v5)))) % 14.42/2.70 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 14.42/2.70 | ! [v5: int] : (v5 = 0 | ~ (inverse_image3(v0, v1, v2) = v4) | ~ % 14.42/2.70 | (member(v3, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 14.42/2.70 | | ? [v6: int] : ( ~ (v6 = 0) & member(v3, v2) = v6) | ! [v6: $i] : % 14.42/2.70 | ( ~ (apply(v0, v3, v6) = 0) | ~ $i(v6) | ? [v7: int] : ( ~ (v7 = 0) % 14.42/2.70 | & member(v6, v1) = v7))) % 14.42/2.70 | % 14.42/2.70 | ALPHA: (function-axioms) implies: % 14.42/2.71 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 14.42/2.71 | : ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, % 14.42/2.71 | v2) = v0)) % 14.42/2.71 | % 14.42/2.71 | DELTA: instantiating (thIIa09) with fresh symbols all_32_0, all_32_1, % 14.42/2.71 | all_32_2, all_32_3, all_32_4, all_32_5, all_32_6 gives: % 14.42/2.71 | (11) ~ (all_32_0 = 0) & inverse_image3(all_32_6, all_32_2, all_32_5) = % 14.42/2.71 | all_32_1 & image3(all_32_6, all_32_3, all_32_4) = all_32_2 & % 14.42/2.71 | injective(all_32_6, all_32_5, all_32_4) = 0 & maps(all_32_6, all_32_5, % 14.42/2.71 | all_32_4) = 0 & equal_set(all_32_1, all_32_3) = all_32_0 & % 14.42/2.71 | subset(all_32_3, all_32_5) = 0 & $i(all_32_1) & $i(all_32_2) & % 14.42/2.71 | $i(all_32_3) & $i(all_32_4) & $i(all_32_5) & $i(all_32_6) % 14.42/2.71 | % 14.42/2.71 | ALPHA: (11) implies: % 14.42/2.71 | (12) ~ (all_32_0 = 0) % 14.42/2.71 | (13) $i(all_32_6) % 14.42/2.71 | (14) $i(all_32_5) % 14.42/2.71 | (15) $i(all_32_4) % 14.42/2.71 | (16) $i(all_32_3) % 14.42/2.71 | (17) $i(all_32_2) % 14.42/2.71 | (18) $i(all_32_1) % 14.42/2.71 | (19) subset(all_32_3, all_32_5) = 0 % 14.42/2.71 | (20) equal_set(all_32_1, all_32_3) = all_32_0 % 14.42/2.71 | (21) maps(all_32_6, all_32_5, all_32_4) = 0 % 14.42/2.71 | (22) injective(all_32_6, all_32_5, all_32_4) = 0 % 14.42/2.71 | (23) image3(all_32_6, all_32_3, all_32_4) = all_32_2 % 14.42/2.71 | (24) inverse_image3(all_32_6, all_32_2, all_32_5) = all_32_1 % 14.42/2.71 | % 14.42/2.71 | GROUND_INST: instantiating (1) with all_32_3, all_32_5, simplifying with (14), % 14.42/2.71 | (16), (19) gives: % 14.42/2.71 | (25) ! [v0: $i] : ( ~ (member(v0, all_32_3) = 0) | ~ $i(v0) | member(v0, % 14.42/2.71 | all_32_5) = 0) % 14.42/2.71 | % 14.42/2.71 | GROUND_INST: instantiating (3) with all_32_1, all_32_3, all_32_0, simplifying % 14.42/2.71 | with (16), (18), (20) gives: % 14.42/2.71 | (26) all_32_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_32_1, % 14.42/2.71 | all_32_3) = v0 & subset(all_32_3, all_32_1) = v1 & ( ~ (v1 = 0) | % 14.42/2.71 | ~ (v0 = 0))) % 14.42/2.71 | % 14.42/2.71 | GROUND_INST: instantiating (4) with all_32_6, all_32_5, all_32_4, simplifying % 14.42/2.71 | with (13), (14), (15), (21) gives: % 14.42/2.72 | (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 14.42/2.72 | (apply(all_32_6, v0, v2) = 0) | ~ (apply(all_32_6, v0, v1) = 0) | % 14.42/2.72 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? % 14.42/2.72 | [v5: any] : (member(v2, all_32_4) = v5 & member(v1, all_32_4) = v4 & % 14.42/2.72 | member(v0, all_32_5) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = % 14.42/2.72 | 0)))) & ! [v0: $i] : ( ~ (member(v0, all_32_5) = 0) | ~ % 14.42/2.72 | $i(v0) | ? [v1: $i] : (apply(all_32_6, v0, v1) = 0 & member(v1, % 14.42/2.72 | all_32_4) = 0 & $i(v1))) % 14.42/2.72 | % 14.42/2.72 | ALPHA: (27) implies: % 14.42/2.72 | (28) ! [v0: $i] : ( ~ (member(v0, all_32_5) = 0) | ~ $i(v0) | ? [v1: $i] % 14.42/2.72 | : (apply(all_32_6, v0, v1) = 0 & member(v1, all_32_4) = 0 & $i(v1))) % 14.42/2.72 | % 14.42/2.72 | GROUND_INST: instantiating (5) with all_32_6, all_32_5, all_32_4, simplifying % 14.42/2.72 | with (13), (14), (15), (22) gives: % 14.42/2.72 | (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 14.42/2.72 | (apply(all_32_6, v1, v2) = 0) | ~ (apply(all_32_6, v0, v2) = 0) | % 14.42/2.72 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? % 14.42/2.72 | [v5: any] : (member(v2, all_32_4) = v5 & member(v1, all_32_5) = v4 & % 14.42/2.72 | member(v0, all_32_5) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = % 14.42/2.72 | 0)))) % 14.42/2.72 | % 14.42/2.72 | BETA: splitting (26) gives: % 14.42/2.72 | % 14.42/2.72 | Case 1: % 14.42/2.72 | | % 14.42/2.72 | | (30) all_32_0 = 0 % 14.42/2.72 | | % 14.42/2.72 | | REDUCE: (12), (30) imply: % 14.42/2.72 | | (31) $false % 14.42/2.72 | | % 14.42/2.72 | | CLOSE: (31) is inconsistent. % 14.42/2.72 | | % 14.42/2.72 | Case 2: % 14.42/2.72 | | % 14.42/2.72 | | (32) ? [v0: any] : ? [v1: any] : (subset(all_32_1, all_32_3) = v0 & % 14.42/2.72 | | subset(all_32_3, all_32_1) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 14.42/2.72 | | % 14.42/2.72 | | DELTA: instantiating (32) with fresh symbols all_45_0, all_45_1 gives: % 14.42/2.72 | | (33) subset(all_32_1, all_32_3) = all_45_1 & subset(all_32_3, all_32_1) = % 14.42/2.72 | | all_45_0 & ( ~ (all_45_0 = 0) | ~ (all_45_1 = 0)) % 14.42/2.72 | | % 14.42/2.72 | | ALPHA: (33) implies: % 14.42/2.72 | | (34) subset(all_32_3, all_32_1) = all_45_0 % 14.42/2.72 | | (35) subset(all_32_1, all_32_3) = all_45_1 % 14.42/2.72 | | (36) ~ (all_45_0 = 0) | ~ (all_45_1 = 0) % 14.42/2.72 | | % 14.42/2.72 | | GROUND_INST: instantiating (2) with all_32_3, all_32_1, all_45_0, % 14.42/2.72 | | simplifying with (16), (18), (34) gives: % 14.42/2.72 | | (37) all_45_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 14.42/2.72 | | member(v0, all_32_1) = v1 & member(v0, all_32_3) = 0 & $i(v0)) % 14.42/2.72 | | % 14.42/2.72 | | GROUND_INST: instantiating (2) with all_32_1, all_32_3, all_45_1, % 14.42/2.72 | | simplifying with (16), (18), (35) gives: % 14.42/2.72 | | (38) all_45_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 14.42/2.72 | | member(v0, all_32_1) = 0 & member(v0, all_32_3) = v1 & $i(v0)) % 14.42/2.72 | | % 14.42/2.72 | | BETA: splitting (36) gives: % 14.42/2.72 | | % 14.42/2.72 | | Case 1: % 14.42/2.72 | | | % 14.42/2.72 | | | (39) ~ (all_45_0 = 0) % 14.42/2.72 | | | % 14.42/2.72 | | | BETA: splitting (37) gives: % 14.42/2.72 | | | % 14.42/2.72 | | | Case 1: % 14.42/2.72 | | | | % 14.42/2.72 | | | | (40) all_45_0 = 0 % 14.42/2.72 | | | | % 14.42/2.72 | | | | REDUCE: (39), (40) imply: % 14.42/2.72 | | | | (41) $false % 14.42/2.72 | | | | % 14.42/2.72 | | | | CLOSE: (41) is inconsistent. % 14.42/2.72 | | | | % 14.42/2.72 | | | Case 2: % 14.42/2.72 | | | | % 14.42/2.73 | | | | (42) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_1) % 14.42/2.73 | | | | = v1 & member(v0, all_32_3) = 0 & $i(v0)) % 14.42/2.73 | | | | % 14.42/2.73 | | | | DELTA: instantiating (42) with fresh symbols all_58_0, all_58_1 gives: % 14.42/2.73 | | | | (43) ~ (all_58_0 = 0) & member(all_58_1, all_32_1) = all_58_0 & % 14.42/2.73 | | | | member(all_58_1, all_32_3) = 0 & $i(all_58_1) % 14.42/2.73 | | | | % 14.42/2.73 | | | | ALPHA: (43) implies: % 14.42/2.73 | | | | (44) ~ (all_58_0 = 0) % 14.42/2.73 | | | | (45) $i(all_58_1) % 14.42/2.73 | | | | (46) member(all_58_1, all_32_3) = 0 % 14.42/2.73 | | | | (47) member(all_58_1, all_32_1) = all_58_0 % 14.42/2.73 | | | | % 14.42/2.73 | | | | GROUND_INST: instantiating (25) with all_58_1, simplifying with (45), % 14.42/2.73 | | | | (46) gives: % 14.42/2.73 | | | | (48) member(all_58_1, all_32_5) = 0 % 14.42/2.73 | | | | % 14.42/2.73 | | | | GROUND_INST: instantiating (9) with all_32_6, all_32_2, all_32_5, % 14.42/2.73 | | | | all_58_1, all_32_1, all_58_0, simplifying with (13), (14), % 14.42/2.73 | | | | (17), (24), (45), (47) gives: % 14.42/2.73 | | | | (49) all_58_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_58_1, % 14.42/2.73 | | | | all_32_5) = v0) | ! [v0: $i] : ( ~ (apply(all_32_6, % 14.42/2.73 | | | | all_58_1, v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = % 14.42/2.73 | | | | 0) & member(v0, all_32_2) = v1)) % 14.42/2.73 | | | | % 14.42/2.73 | | | | BETA: splitting (49) gives: % 14.42/2.73 | | | | % 14.42/2.73 | | | | Case 1: % 14.42/2.73 | | | | | % 14.42/2.73 | | | | | (50) all_58_0 = 0 % 14.42/2.73 | | | | | % 14.42/2.73 | | | | | REDUCE: (44), (50) imply: % 14.42/2.73 | | | | | (51) $false % 14.42/2.73 | | | | | % 14.42/2.73 | | | | | CLOSE: (51) is inconsistent. % 14.42/2.73 | | | | | % 14.42/2.73 | | | | Case 2: % 14.42/2.73 | | | | | % 14.42/2.73 | | | | | (52) ? [v0: int] : ( ~ (v0 = 0) & member(all_58_1, all_32_5) = v0) % 14.42/2.73 | | | | | | ! [v0: $i] : ( ~ (apply(all_32_6, all_58_1, v0) = 0) | ~ % 14.42/2.73 | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_2) % 14.42/2.73 | | | | | = v1)) % 14.42/2.73 | | | | | % 14.42/2.73 | | | | | BETA: splitting (52) gives: % 14.42/2.73 | | | | | % 14.42/2.73 | | | | | Case 1: % 14.42/2.73 | | | | | | % 14.42/2.73 | | | | | | (53) ? [v0: int] : ( ~ (v0 = 0) & member(all_58_1, all_32_5) = % 14.42/2.73 | | | | | | v0) % 14.42/2.73 | | | | | | % 14.42/2.73 | | | | | | DELTA: instantiating (53) with fresh symbol all_73_0 gives: % 14.42/2.73 | | | | | | (54) ~ (all_73_0 = 0) & member(all_58_1, all_32_5) = all_73_0 % 14.42/2.73 | | | | | | % 14.42/2.73 | | | | | | ALPHA: (54) implies: % 14.42/2.73 | | | | | | (55) ~ (all_73_0 = 0) % 14.42/2.73 | | | | | | (56) member(all_58_1, all_32_5) = all_73_0 % 14.42/2.73 | | | | | | % 14.42/2.73 | | | | | | GROUND_INST: instantiating (10) with 0, all_73_0, all_32_5, % 14.42/2.73 | | | | | | all_58_1, simplifying with (48), (56) gives: % 14.42/2.73 | | | | | | (57) all_73_0 = 0 % 14.42/2.73 | | | | | | % 14.42/2.73 | | | | | | REDUCE: (55), (57) imply: % 14.42/2.73 | | | | | | (58) $false % 14.42/2.73 | | | | | | % 14.42/2.73 | | | | | | CLOSE: (58) is inconsistent. % 14.42/2.73 | | | | | | % 14.42/2.73 | | | | | Case 2: % 14.42/2.73 | | | | | | % 14.42/2.73 | | | | | | (59) ! [v0: $i] : ( ~ (apply(all_32_6, all_58_1, v0) = 0) | ~ % 14.42/2.73 | | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 14.42/2.73 | | | | | | all_32_2) = v1)) % 14.42/2.73 | | | | | | % 14.42/2.73 | | | | | | GROUND_INST: instantiating (28) with all_58_1, simplifying with % 14.42/2.73 | | | | | | (45), (48) gives: % 14.42/2.73 | | | | | | (60) ? [v0: $i] : (apply(all_32_6, all_58_1, v0) = 0 & % 14.42/2.73 | | | | | | member(v0, all_32_4) = 0 & $i(v0)) % 14.42/2.73 | | | | | | % 14.42/2.73 | | | | | | DELTA: instantiating (60) with fresh symbol all_78_0 gives: % 14.42/2.73 | | | | | | (61) apply(all_32_6, all_58_1, all_78_0) = 0 & member(all_78_0, % 14.42/2.73 | | | | | | all_32_4) = 0 & $i(all_78_0) % 14.42/2.73 | | | | | | % 14.42/2.73 | | | | | | ALPHA: (61) implies: % 14.42/2.73 | | | | | | (62) $i(all_78_0) % 14.42/2.73 | | | | | | (63) member(all_78_0, all_32_4) = 0 % 14.42/2.73 | | | | | | (64) apply(all_32_6, all_58_1, all_78_0) = 0 % 14.42/2.73 | | | | | | % 14.42/2.73 | | | | | | GROUND_INST: instantiating (59) with all_78_0, simplifying with % 14.42/2.73 | | | | | | (62), (64) gives: % 14.42/2.73 | | | | | | (65) ? [v0: int] : ( ~ (v0 = 0) & member(all_78_0, all_32_2) = % 14.42/2.73 | | | | | | v0) % 14.42/2.73 | | | | | | % 14.42/2.73 | | | | | | DELTA: instantiating (65) with fresh symbol all_85_0 gives: % 14.42/2.73 | | | | | | (66) ~ (all_85_0 = 0) & member(all_78_0, all_32_2) = all_85_0 % 14.42/2.73 | | | | | | % 14.42/2.73 | | | | | | ALPHA: (66) implies: % 14.42/2.73 | | | | | | (67) ~ (all_85_0 = 0) % 14.42/2.73 | | | | | | (68) member(all_78_0, all_32_2) = all_85_0 % 14.42/2.73 | | | | | | % 14.42/2.73 | | | | | | GROUND_INST: instantiating (7) with all_32_6, all_32_3, all_32_4, % 14.42/2.73 | | | | | | all_78_0, all_32_2, all_85_0, simplifying with (13), % 14.42/2.73 | | | | | | (15), (16), (23), (62), (68) gives: % 14.42/2.74 | | | | | | (69) all_85_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 14.42/2.74 | | | | | | member(all_78_0, all_32_4) = v0) | ! [v0: $i] : ( ~ % 14.42/2.74 | | | | | | (apply(all_32_6, v0, all_78_0) = 0) | ~ $i(v0) | ? [v1: % 14.42/2.74 | | | | | | int] : ( ~ (v1 = 0) & member(v0, all_32_3) = v1)) % 14.42/2.74 | | | | | | % 14.42/2.74 | | | | | | BETA: splitting (69) gives: % 14.42/2.74 | | | | | | % 14.42/2.74 | | | | | | Case 1: % 14.42/2.74 | | | | | | | % 14.42/2.74 | | | | | | | (70) all_85_0 = 0 % 14.42/2.74 | | | | | | | % 14.42/2.74 | | | | | | | REDUCE: (67), (70) imply: % 14.42/2.74 | | | | | | | (71) $false % 14.42/2.74 | | | | | | | % 14.42/2.74 | | | | | | | CLOSE: (71) is inconsistent. % 14.42/2.74 | | | | | | | % 14.42/2.74 | | | | | | Case 2: % 14.42/2.74 | | | | | | | % 14.42/2.74 | | | | | | | (72) ? [v0: int] : ( ~ (v0 = 0) & member(all_78_0, all_32_4) = % 14.42/2.74 | | | | | | | v0) | ! [v0: $i] : ( ~ (apply(all_32_6, v0, all_78_0) = % 14.42/2.74 | | | | | | | 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 14.42/2.74 | | | | | | | member(v0, all_32_3) = v1)) % 14.42/2.74 | | | | | | | % 14.42/2.74 | | | | | | | BETA: splitting (72) gives: % 14.42/2.74 | | | | | | | % 14.42/2.74 | | | | | | | Case 1: % 14.42/2.74 | | | | | | | | % 14.42/2.74 | | | | | | | | (73) ? [v0: int] : ( ~ (v0 = 0) & member(all_78_0, all_32_4) % 14.42/2.74 | | | | | | | | = v0) % 14.42/2.74 | | | | | | | | % 14.42/2.74 | | | | | | | | DELTA: instantiating (73) with fresh symbol all_103_0 gives: % 14.42/2.74 | | | | | | | | (74) ~ (all_103_0 = 0) & member(all_78_0, all_32_4) = % 14.42/2.74 | | | | | | | | all_103_0 % 14.42/2.74 | | | | | | | | % 14.42/2.74 | | | | | | | | ALPHA: (74) implies: % 14.42/2.74 | | | | | | | | (75) ~ (all_103_0 = 0) % 14.42/2.74 | | | | | | | | (76) member(all_78_0, all_32_4) = all_103_0 % 14.42/2.74 | | | | | | | | % 14.42/2.74 | | | | | | | | GROUND_INST: instantiating (10) with 0, all_103_0, all_32_4, % 14.42/2.74 | | | | | | | | all_78_0, simplifying with (63), (76) gives: % 14.42/2.74 | | | | | | | | (77) all_103_0 = 0 % 14.42/2.74 | | | | | | | | % 14.42/2.74 | | | | | | | | REDUCE: (75), (77) imply: % 14.42/2.74 | | | | | | | | (78) $false % 14.42/2.74 | | | | | | | | % 14.42/2.74 | | | | | | | | CLOSE: (78) is inconsistent. % 14.42/2.74 | | | | | | | | % 14.42/2.74 | | | | | | | Case 2: % 14.42/2.74 | | | | | | | | % 14.42/2.74 | | | | | | | | (79) ! [v0: $i] : ( ~ (apply(all_32_6, v0, all_78_0) = 0) | % 14.42/2.74 | | | | | | | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 14.42/2.74 | | | | | | | | all_32_3) = v1)) % 14.42/2.74 | | | | | | | | % 14.42/2.74 | | | | | | | | GROUND_INST: instantiating (79) with all_58_1, simplifying with % 14.42/2.74 | | | | | | | | (45), (64) gives: % 14.42/2.74 | | | | | | | | (80) ? [v0: int] : ( ~ (v0 = 0) & member(all_58_1, all_32_3) % 14.42/2.74 | | | | | | | | = v0) % 14.42/2.74 | | | | | | | | % 14.42/2.74 | | | | | | | | DELTA: instantiating (80) with fresh symbol all_104_0 gives: % 14.42/2.74 | | | | | | | | (81) ~ (all_104_0 = 0) & member(all_58_1, all_32_3) = % 14.42/2.74 | | | | | | | | all_104_0 % 14.42/2.74 | | | | | | | | % 14.42/2.74 | | | | | | | | ALPHA: (81) implies: % 14.42/2.74 | | | | | | | | (82) ~ (all_104_0 = 0) % 14.42/2.74 | | | | | | | | (83) member(all_58_1, all_32_3) = all_104_0 % 14.42/2.74 | | | | | | | | % 14.42/2.74 | | | | | | | | GROUND_INST: instantiating (10) with 0, all_104_0, all_32_3, % 14.42/2.74 | | | | | | | | all_58_1, simplifying with (46), (83) gives: % 14.42/2.74 | | | | | | | | (84) all_104_0 = 0 % 14.42/2.74 | | | | | | | | % 14.42/2.74 | | | | | | | | REDUCE: (82), (84) imply: % 14.42/2.74 | | | | | | | | (85) $false % 14.42/2.74 | | | | | | | | % 14.42/2.74 | | | | | | | | CLOSE: (85) is inconsistent. % 14.42/2.74 | | | | | | | | % 14.42/2.74 | | | | | | | End of split % 14.42/2.74 | | | | | | | % 14.42/2.74 | | | | | | End of split % 14.42/2.74 | | | | | | % 14.42/2.74 | | | | | End of split % 14.42/2.74 | | | | | % 14.42/2.74 | | | | End of split % 14.42/2.74 | | | | % 14.42/2.74 | | | End of split % 14.42/2.74 | | | % 14.42/2.74 | | Case 2: % 14.42/2.74 | | | % 14.42/2.74 | | | (86) ~ (all_45_1 = 0) % 14.42/2.74 | | | % 14.42/2.74 | | | BETA: splitting (38) gives: % 14.42/2.74 | | | % 14.42/2.74 | | | Case 1: % 14.42/2.74 | | | | % 14.42/2.74 | | | | (87) all_45_1 = 0 % 14.42/2.74 | | | | % 14.42/2.74 | | | | REDUCE: (86), (87) imply: % 14.42/2.74 | | | | (88) $false % 14.42/2.74 | | | | % 14.42/2.74 | | | | CLOSE: (88) is inconsistent. % 14.42/2.74 | | | | % 14.42/2.74 | | | Case 2: % 14.42/2.74 | | | | % 14.78/2.74 | | | | (89) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_1) % 14.78/2.74 | | | | = 0 & member(v0, all_32_3) = v1 & $i(v0)) % 14.78/2.74 | | | | % 14.78/2.74 | | | | DELTA: instantiating (89) with fresh symbols all_58_0, all_58_1 gives: % 14.78/2.74 | | | | (90) ~ (all_58_0 = 0) & member(all_58_1, all_32_1) = 0 & % 14.78/2.74 | | | | member(all_58_1, all_32_3) = all_58_0 & $i(all_58_1) % 14.78/2.74 | | | | % 14.78/2.74 | | | | ALPHA: (90) implies: % 14.78/2.74 | | | | (91) ~ (all_58_0 = 0) % 14.78/2.74 | | | | (92) $i(all_58_1) % 14.78/2.74 | | | | (93) member(all_58_1, all_32_3) = all_58_0 % 14.78/2.74 | | | | (94) member(all_58_1, all_32_1) = 0 % 14.78/2.74 | | | | % 14.78/2.74 | | | | GROUND_INST: instantiating (8) with all_32_6, all_32_2, all_32_5, % 14.78/2.74 | | | | all_58_1, all_32_1, simplifying with (13), (14), (17), % 14.78/2.74 | | | | (24), (92), (94) gives: % 14.78/2.74 | | | | (95) member(all_58_1, all_32_5) = 0 & ? [v0: $i] : (apply(all_32_6, % 14.78/2.74 | | | | all_58_1, v0) = 0 & member(v0, all_32_2) = 0 & $i(v0)) % 14.78/2.74 | | | | % 14.78/2.74 | | | | ALPHA: (95) implies: % 14.78/2.74 | | | | (96) member(all_58_1, all_32_5) = 0 % 14.78/2.74 | | | | (97) ? [v0: $i] : (apply(all_32_6, all_58_1, v0) = 0 & member(v0, % 14.78/2.74 | | | | all_32_2) = 0 & $i(v0)) % 14.78/2.74 | | | | % 14.78/2.74 | | | | DELTA: instantiating (97) with fresh symbol all_67_0 gives: % 14.78/2.74 | | | | (98) apply(all_32_6, all_58_1, all_67_0) = 0 & member(all_67_0, % 14.78/2.74 | | | | all_32_2) = 0 & $i(all_67_0) % 14.78/2.74 | | | | % 14.78/2.74 | | | | ALPHA: (98) implies: % 14.78/2.74 | | | | (99) $i(all_67_0) % 14.78/2.74 | | | | (100) member(all_67_0, all_32_2) = 0 % 14.78/2.74 | | | | (101) apply(all_32_6, all_58_1, all_67_0) = 0 % 14.78/2.74 | | | | % 14.78/2.75 | | | | GROUND_INST: instantiating (6) with all_32_6, all_32_3, all_32_4, % 14.78/2.75 | | | | all_67_0, all_32_2, simplifying with (13), (15), (16), % 14.78/2.75 | | | | (23), (99), (100) gives: % 14.78/2.75 | | | | (102) member(all_67_0, all_32_4) = 0 & ? [v0: $i] : (apply(all_32_6, % 14.78/2.75 | | | | v0, all_67_0) = 0 & member(v0, all_32_3) = 0 & $i(v0)) % 14.78/2.75 | | | | % 14.78/2.75 | | | | ALPHA: (102) implies: % 14.78/2.75 | | | | (103) member(all_67_0, all_32_4) = 0 % 14.78/2.75 | | | | (104) ? [v0: $i] : (apply(all_32_6, v0, all_67_0) = 0 & member(v0, % 14.78/2.75 | | | | all_32_3) = 0 & $i(v0)) % 14.78/2.75 | | | | % 14.78/2.75 | | | | DELTA: instantiating (104) with fresh symbol all_75_0 gives: % 14.78/2.75 | | | | (105) apply(all_32_6, all_75_0, all_67_0) = 0 & member(all_75_0, % 14.78/2.75 | | | | all_32_3) = 0 & $i(all_75_0) % 14.78/2.75 | | | | % 14.78/2.75 | | | | ALPHA: (105) implies: % 14.78/2.75 | | | | (106) $i(all_75_0) % 14.78/2.75 | | | | (107) member(all_75_0, all_32_3) = 0 % 14.78/2.75 | | | | (108) apply(all_32_6, all_75_0, all_67_0) = 0 % 14.78/2.75 | | | | % 14.78/2.75 | | | | GROUND_INST: instantiating (25) with all_75_0, simplifying with (106), % 14.78/2.75 | | | | (107) gives: % 14.78/2.75 | | | | (109) member(all_75_0, all_32_5) = 0 % 14.78/2.75 | | | | % 14.78/2.75 | | | | GROUND_INST: instantiating (29) with all_75_0, all_58_1, all_67_0, % 14.78/2.75 | | | | simplifying with (92), (99), (101), (106), (108) gives: % 14.78/2.75 | | | | (110) all_75_0 = all_58_1 | ? [v0: any] : ? [v1: any] : ? [v2: % 14.78/2.75 | | | | any] : (member(all_75_0, all_32_5) = v0 & member(all_67_0, % 14.78/2.75 | | | | all_32_4) = v2 & member(all_58_1, all_32_5) = v1 & ( ~ (v2 % 14.78/2.75 | | | | = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 14.78/2.75 | | | | % 14.78/2.75 | | | | BETA: splitting (110) gives: % 14.78/2.75 | | | | % 14.78/2.75 | | | | Case 1: % 14.78/2.75 | | | | | % 14.78/2.75 | | | | | (111) all_75_0 = all_58_1 % 14.78/2.75 | | | | | % 14.78/2.75 | | | | | REDUCE: (107), (111) imply: % 14.78/2.75 | | | | | (112) member(all_58_1, all_32_3) = 0 % 14.78/2.75 | | | | | % 14.78/2.75 | | | | | GROUND_INST: instantiating (10) with all_58_0, 0, all_32_3, all_58_1, % 14.78/2.75 | | | | | simplifying with (93), (112) gives: % 14.78/2.75 | | | | | (113) all_58_0 = 0 % 14.78/2.75 | | | | | % 14.78/2.75 | | | | | REDUCE: (91), (113) imply: % 14.78/2.75 | | | | | (114) $false % 14.78/2.75 | | | | | % 14.78/2.75 | | | | | CLOSE: (114) is inconsistent. % 14.78/2.75 | | | | | % 14.78/2.75 | | | | Case 2: % 14.78/2.75 | | | | | % 14.78/2.75 | | | | | (115) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 14.78/2.75 | | | | | (member(all_75_0, all_32_5) = v0 & member(all_67_0, all_32_4) % 14.78/2.75 | | | | | = v2 & member(all_58_1, all_32_5) = v1 & ( ~ (v2 = 0) | ~ % 14.78/2.75 | | | | | (v1 = 0) | ~ (v0 = 0))) % 14.78/2.75 | | | | | % 14.78/2.75 | | | | | DELTA: instantiating (115) with fresh symbols all_93_0, all_93_1, % 14.78/2.75 | | | | | all_93_2 gives: % 14.78/2.75 | | | | | (116) member(all_75_0, all_32_5) = all_93_2 & member(all_67_0, % 14.78/2.75 | | | | | all_32_4) = all_93_0 & member(all_58_1, all_32_5) = % 14.78/2.75 | | | | | all_93_1 & ( ~ (all_93_0 = 0) | ~ (all_93_1 = 0) | ~ % 14.78/2.75 | | | | | (all_93_2 = 0)) % 14.78/2.75 | | | | | % 14.78/2.75 | | | | | ALPHA: (116) implies: % 14.78/2.75 | | | | | (117) member(all_58_1, all_32_5) = all_93_1 % 14.78/2.75 | | | | | (118) member(all_67_0, all_32_4) = all_93_0 % 14.78/2.75 | | | | | (119) member(all_75_0, all_32_5) = all_93_2 % 14.78/2.75 | | | | | (120) ~ (all_93_0 = 0) | ~ (all_93_1 = 0) | ~ (all_93_2 = 0) % 14.78/2.75 | | | | | % 14.78/2.75 | | | | | GROUND_INST: instantiating (10) with 0, all_93_1, all_32_5, all_58_1, % 14.78/2.75 | | | | | simplifying with (96), (117) gives: % 14.78/2.75 | | | | | (121) all_93_1 = 0 % 14.78/2.75 | | | | | % 14.78/2.75 | | | | | GROUND_INST: instantiating (10) with 0, all_93_0, all_32_4, all_67_0, % 14.78/2.75 | | | | | simplifying with (103), (118) gives: % 14.78/2.75 | | | | | (122) all_93_0 = 0 % 14.78/2.75 | | | | | % 14.78/2.75 | | | | | GROUND_INST: instantiating (10) with 0, all_93_2, all_32_5, all_75_0, % 14.78/2.75 | | | | | simplifying with (109), (119) gives: % 14.78/2.75 | | | | | (123) all_93_2 = 0 % 14.78/2.75 | | | | | % 14.78/2.75 | | | | | BETA: splitting (120) gives: % 14.78/2.75 | | | | | % 14.78/2.75 | | | | | Case 1: % 14.78/2.75 | | | | | | % 14.78/2.75 | | | | | | (124) ~ (all_93_0 = 0) % 14.78/2.75 | | | | | | % 14.78/2.75 | | | | | | REDUCE: (122), (124) imply: % 14.78/2.75 | | | | | | (125) $false % 14.78/2.75 | | | | | | % 14.78/2.75 | | | | | | CLOSE: (125) is inconsistent. % 14.78/2.75 | | | | | | % 14.78/2.75 | | | | | Case 2: % 14.78/2.75 | | | | | | % 14.78/2.75 | | | | | | (126) ~ (all_93_1 = 0) | ~ (all_93_2 = 0) % 14.78/2.75 | | | | | | % 14.78/2.75 | | | | | | BETA: splitting (126) gives: % 14.78/2.75 | | | | | | % 14.78/2.75 | | | | | | Case 1: % 14.78/2.75 | | | | | | | % 14.78/2.75 | | | | | | | (127) ~ (all_93_1 = 0) % 14.78/2.75 | | | | | | | % 14.78/2.75 | | | | | | | REDUCE: (121), (127) imply: % 14.78/2.75 | | | | | | | (128) $false % 14.78/2.75 | | | | | | | % 14.78/2.75 | | | | | | | CLOSE: (128) is inconsistent. % 14.78/2.75 | | | | | | | % 14.78/2.75 | | | | | | Case 2: % 14.78/2.75 | | | | | | | % 14.78/2.75 | | | | | | | (129) ~ (all_93_2 = 0) % 14.78/2.75 | | | | | | | % 14.78/2.75 | | | | | | | REDUCE: (123), (129) imply: % 14.78/2.75 | | | | | | | (130) $false % 14.78/2.75 | | | | | | | % 14.78/2.75 | | | | | | | CLOSE: (130) is inconsistent. % 14.78/2.75 | | | | | | | % 14.78/2.75 | | | | | | End of split % 14.78/2.75 | | | | | | % 14.78/2.75 | | | | | End of split % 14.78/2.75 | | | | | % 14.78/2.75 | | | | End of split % 14.78/2.75 | | | | % 14.78/2.75 | | | End of split % 14.78/2.75 | | | % 14.78/2.75 | | End of split % 14.78/2.75 | | % 14.78/2.75 | End of split % 14.78/2.75 | % 14.78/2.75 End of proof % 14.78/2.75 % SZS output end Proof for theBenchmark % 14.78/2.75 % 14.78/2.75 2137ms %------------------------------------------------------------------------------